Related papers: On Ulam type stability for nonlinear implicit frac…
For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…
Using the $\psi-$Hilfer fractional derivative, we present a study of the Hyers-Ulam-Rassias stability and the Hyers-Ulam stability of the fractional Volterra integral-differential equation by means of fixed-point method.
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
In this article, the order of some classes of fractional linear differential equations is determined, based on asymptotic behavior of the solution as time tends to infinity. The order of fractional derivative has been proved to be of great…
We study the existence and uniqueness of solution of a nonlinear Cauchy problem involving the $\psi$-Hilfer fractional derivative. In addition, we discuss the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of its solutions. A few examples…
We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order $0<\beta<1$. From the known structure of the non-smooth solution and by introducing corresponding…
This paper presents the generalized formulations of fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain (FDTD) methods. The fundamental schemes constitute a family of implicit schemes that feature…
Von Neumann established that discretized algebraic equations must be consistent with the differential equations, and must be stable in order to obtain convergent numerical solutions for the given differential equations. The "stability" is…
This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the…
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
The stability of non-isolated equilibria to quasilinear parabolic problems of the form $u' = A(u)u + f(u)$ is established in interpolation spaces (and thus extending previous results relying on maximal regularity). The approach allows full…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
We prove two results concerning an Ulam-type stability problem for homomorphisms between lattices. One of them involves estimates by quite general error functions; the other deals with approximate (join) homomorphisms in terms of certain…
In the present paper by the Fourier transform we show that every linear differential equations of $n$-th order has a solution in $L^1(\Bbb{R})$ which is infinitely differentiable in $\Bbb{R} \setminus \{0\}$. Moreover the Hyers-Ulam…
An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the…
In this paper, we study existence results for initial value problems for hybrid fractional integro-differential equations. Our investigation is based on the Dhage hybrid fixed point theorem. Some fundamental fractional differential…
This technical report replies to the comments of [2] in detail, and corrects a possible mis-interpretation of [1] in terms of the conventional robust stability concept. After defining the robust stability and quadratic stability concepts,…